Almost linearizable control systems
| Autor: | V. I. Korobov |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
0209 industrial biotechnology
Change of variables Control and Optimization Applied Mathematics 010102 general mathematics Linear system 02 engineering and technology 01 natural sciences Constructive Controllability Nonlinear system 020901 industrial engineering & automation Control and Systems Engineering Linearization Control system Signal Processing Applied mathematics Boundary value problem 0101 mathematics Mathematics |
| Zdroj: | Mathematics of Control, Signals, and Systems. 33:473-497 |
| ISSN: | 1435-568X 0932-4194 |
| DOI: | 10.1007/s00498-021-00288-w |
| Popis: | We extend the approach based on the linearization of triangular systems to new classes of non-linearizable control systems that are almost linearizable. This means that there exists a change of variables and control mapping all but one equations of the initial nonlinear system to a linear system. We show how this property can be used for solving the problem of constructive controllability, i.e., finding trajectories connecting two given points. Namely, we explicitly find a change of variables and control that maps $$n-1$$ equations of the initial system to a linear system. For the remaining first-order nonlinear differential equation, which contains one unknown scalar parameter, the boundary value problem is considered. Once this one-dimensional problem is solved, a trajectory connecting two given points for the initial system is explicitly found. Moreover, we solve the stabilization problem for systems from the proposed classes under additional natural conditions. We give several examples to illustrate a constructive character of our approach. |
| Databáze: | OpenAIRE |
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